The present invention relates to a new and distinct blackberry cultivar designated ‘Galaxy’ and botanically known as Rubus subg. Rubus Watson. This new blackberry cultivar was discovered in Corvallis, Oreg. in August 2003 and originated from a cross between the female blackberry plant ‘ORUS 1393-1’ (unpatented) and the thornless, male parent blackberry plant ‘Triple Crown’ (unpatented). ‘Galaxy’ shares the same parents as ‘Eclipse’ (U.S. Plant patent application Ser. No. 15/731,503) but it was selected one year earlier from a different cross of the same parents. ‘ORUS 1393-1’ (unpatented) was a selection from a cross of the thornless erect blackberry ‘Navaho’ (U.S. Plant Pat. No. 6,679) and a thorny trailing blackberry selection ORUS 1122-1 (unpatented). Therefore, ‘Galaxy’ represents a unique pedigree with all three of the main types of blackberry used in breeding for commercial cultivars represented in its pedigree as it's paternal parent is a hybrid of an erect and trailing blackberry genotype and its maternal parent is a semi-erect blackberry. ‘Galaxy's’ spinelessness was originally derived from ‘Merton Thornless’ (U.S. Plant Pat. No. 571). The original seedling of the new cultivar was asexually propagated at a nursery in Benton County, Oreg. The new cultivar was established in vitro from a cane cutting and microcuttings have been taken and rooted from this sort of culture. The present invention has been found to be stable and reproduce true to type through successive asexual propagations.